Happy maths 2

Happy Maths
Shapes and Data

Written by Mala Kumar
Illustrated by Angie & Upesh


Original Story (English)
Happy Maths - 2
Shapes and Data by Mala Kumar
©Pratham Books, 2007
First Edition 2007

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Illustrations: Angie & Upesh

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Happy Maths - 2
Shapes and Data

Written by
Mala Kumar
Illustrated by
Angie & Upesh


Sankhya and Ganith have been learning a lot of things
in their mathematics class.
Join Sankhya and Ganith in their
happy discoveries about mathematics.
Zzero and Eka are friends of Sankhya and Ganith.
In this book, Sankhya and Ganith learn that different
shapes have different properties. They also try to
understand how to make sense of all the information that
they gather.

2

Sankhya likes to skip.
The last time her brother Ganith counted,
she skipped a hundred and ten times in five minutes!
Ganith tried it too.
He skipped thirty times…
tripped and fell down.
It’s fun to count sometimes.
Numbers are just one part of mathematics.
This book tells you how you can play with mathematics.
You see it can be fun almost all the time.

3


The Funny Cricket Ground
Hello, my name is Zzero.
And this is my friend, Eka. That makes two of us.
With you for company, we will be three. And if you get all
your friends to join us…. why we can be a cricket team,
or a hockey team or even the entire stadium of football
fans, or…. That reminds me, I have to be at the cricket
match between Aryanagar and Bhaskaragram.You see,
I’m the Umpire! I hope you will help me keep count.

The cricket ground in Aryanagar is large. Its boundary is not
clear. Sometimes, the boys put pegs around it at equal distances
and they put a rope around the pegs. The rope becomes the
boundary. If the pegs are put neatly, we get a circle.

4

Sometimes, when one of the boys is a bit lazy and does not measure
the distance between two pegs carefully, the shape of the field
changes. When a match is boring, the crowd stays away.

But when there is an interesting match, the viewers come closer
and closer to the pitch and the field takes on different shapes
depending on which side of the crowd is pushing in stronger!

Most professional cricket grounds should be large enough to
mark an oval boundary measuring 65 metres from the stumps
at either end of the wicket. Official cricket fields in the world
usually measure about 90 to 150 metres across.
5


At Aryanagar, rules keep changing.
Ashwin, the tallest fellow in Aryanagar wants a square field.
Little Meenu wants a small, circular field.
Samir, the strongest boy in Aryanagar wants a large,
pentagon shaped field.

6


1. Draw cricket fields in different shapes. Do all these shapes
have names?
2. If you had to have a cricket ground with straight lines as
boundaries, what is the smallest number of straight lines

that you would require to form a field?
3. If a batsman hits a boundary, he gets four runs. If you were
a batsman, what shape of field would you like to play on?
Why?
4. In a circular field, the stumps on either end of the pitch are
65m from the boundary. The pitch is 20m long. Would you
be able to tell how long the rope of the boundary should
be?

7


A

Try This
In a circle, the centre O is equidistant
from every point on the circle.

65m
10m

O

Pitch length = 20m
Radius of circle=10m + 65m = 75m
Circumference of a circle is given by the formula -

B

Circumference = 2πr

What’s

π?

Pi is a value. When you divide the circumference of a circle by
its diameter, you always get 22/7.
Take any circle. Measure its circumference. Measure its
diameter. Divide the circumference by its diameter.
Answer = 22/7.

What if I take a BIG
circle, Zzero?

8

Try it, Eka, or take a tiny
circle. The answer will
always be the same!


Floor Designs
Sankhya was making a rangoli on the floor.
Ganith did not like it. “Akka, why do you always make rangolis
that look like jalebis? See, I will make a new rangoli.”
Ganith made some straight lines on the mud floor.
Sankhya giggled. “Your rangoli looks like a lot of bricks. I don’t
like that.”

Ganith looked up at the mango tree nearby. He drew a square to
represent the tree.

Sankhya drew a smaller square inside the big square to show the
base of the tree.

9


Ganith went around the garden and brought a huge mound of
flowers for her to decorate the rangoli with.
Sankhya started keeping the flowers on the inner square.
Four flowers fitted side-by-side on one side of the inside square.

After Sankhya had filled the square with flowers, she put flowers
on top of these. She repeated this four times. The rangoli now
looked like a solid tower.
Sankhyapickedupsomemorewhitepowderandstartedhumming
to herself. As she sang, her hands flew on the floor and soon she
had a beautiful figure that had many curves. It did not have any
sharp corners.
“Akka, you are an artist!” said Ganith.

10


1. Do you like to do freehand drawing? Can you draw this
figure without lifting your pencil off the paper or retracing
your lines?

2. Draw the rangoli that Sankhya and Ganith drew and then
decorated with flowers.
3. How many sharp ‘corners’ does this figure have?

4. How many flowers did Sankhya use to decorate the
rangoli?
5. Instead of 4, if Sankhya had used 10 flowers along each
line of the inner square, how many flowers would she
have needed to make a ‘tower’ 10 floors high? (Or you
could say, 10 flowers high!)

11


Zzeros Chatter
ZZero, do you know
what 2D and 3D mean?

Zzero.
o
No, no,
ds for tw
2D stan th, and height
ns. Leng
ns.
dimensio are all dimensio
e
th
asure th
e
and wid
m
o
t

them
We use of an object.
size

Very smart, Zzero!

12

Are they
the
in which N classes
eela and
Suresh stu
dy, Eka?

So 3D means three
dimensions!


So Much Information!
“Today’s weather - warm and sunny throughout the day, heavy
rain expected in the evening,” said a stylish newsreader on
television.
“You better carry your umbrella, Sankhya,” cautioned Amma.
“I think I’ll cut the grass in the backyard tomorrow,” said
Father.
“I’m going to make paper boats of all kinds. Yippee!” danced
Ganith.

13

Data
Data is nothing but information.
Actually, the singular of data is datum. Funny word!
We use data to form opinions, to make arrangements, to organise
matters and to inform others.
Sankhya and her family used the data from the news on television
to organise their time. Mathematical data is very useful too.
We use mathematical data, also called statistics, in many ways.

14


What’s
Average ?

Sankhya likes writing tests. Her marks indicate
whether she has learnt her lessons well.
When she gets ‘above average’ marks
she feels happy.
But what does average mean?
Let’s see. These are the marks out of 100 that Sankhya and her
19 classmates got in the last mathematics examination.
74, 65, 35, 57, 59, 53, 44, 88, 97, 33, 86, 88, 88, 45, 61, 79, 88,
56, 57, 67.
Let us add all these marks.
74+ 65+ 35+ 57+ 59+ 53+ 44+ 88+ 97+ 33+ 86+ 88+
88+ 45+ 61+ 79+ 88+ 56+ 57+ 67=1320.
The number we get when we divide the sum by the number of

students is called Arithmetic Mean, or average.
1320 divided by 20=66.
Mean score in Sankhya’s class in Mathematics is 66. Anyone who
gets around this has scored average marks. Students who get
higher marks than the mean have scored above average marks.
Students who score much less than the mean need to do much
better in the next examination!
15


Mode
What have most students in Sankhya’s class scored?

Let’s put the marks in ascending order, that is, from the lowest
to the highest.
Mode is the figure that appears most often in the list.
In the list 88 is the Mode.
Median
Median is the number that appears in the middle of the list after
you have put it in descending or ascending order.
7 5 9 61 6
8
57 5
5 6
33
88 88 8 97
6
5
8
35 44 45 53

77
8
4 79 86

In a group of 20 numbers, the 10th and 11th numbers are in the
middle. Median is the value between these two numbers that is
between 61 and 65.
Median in this example is 63. (61+65 / 2 =126 / 2=63)

16


Sankhya is Confused
“In the Class 10 Board examinations, 50% of students have
passed. 10% of students who have passed are from the Urban
centres in the State. While 80% of girls who have passed have
scored first class marks only 70 % of boys have secured first
class. …..” Sankhya read from the day’s newspaper.
“How did the newspaper get so much information in one day?
No one came to Aryanagar to find out. So how do they know how
the boys and girls in our school have fared in the examinations?”
asked a very confused Sankhya.
“Forget that, Sankhi, come here and help me sort these answersheets,” requested Amma.
‘Percent’ comes from the
Latin
Per Centum. Centum me
ans 100.
Percentage means ‘numb
er of
parts per hundred’. The

symbol for
percentage is %.50% me
ans
50 out of 100.

17


Sankhya’s mother is a geography teacher in Aryanagar
Vidyamandir.
“Put all Class 5 papers here, Class 4 papers in this pile, and
Class 6 papers here.”
Mother and daughter counted the number of answer copies
in each class. Sankhya spent the day helping her mother to fill
up the record book that had columns for Name, Marks and
Comments.
At the end of the day, Sankhya could guess
some things clearly:
• There were more number of students in Class 4 than in
Class 5.
• The Class 6 answer papers were thicker than the answer
papers of Class 4.
• More girls in Class 6 had passed than boys.
• Equal number of girls and boys had passed in Class 4.
18


Now, lets go back to the newspaper.
Schools send their lists with the names of students to a Central
Board. After the papers are corrected, the Central Board makes

a list with the names of all the students and their marks.
People called Analysts or Statisticians read this information,
understand it, and write it in the form of tables so that we can
understand the information easily.
The table is given to newspapers, television channels and to all
the schools in the country immediately.
Over 6,00,000 students wrote the Class 10 examinations in the
CBSE Board in 2006.
“And lakhs of students must have written the Class 10 exams of
other Boards too, isn’t it ?” asked Sankhya.
CENTRAL
BOARD

ANALYST

19


“Yes, Sankhya. Now call Ganith and I’ll teach you how to make
rotis.”

Sankhya’s roti looked like this. (An Oblong)

Amma’s roti looked like this.(Perfect Circle)

Ganith’s roti looked like this. (Shapeless)

20

1. If the full roti represents the 100 percent of students who
took up the Class X CBSE examination, what part of the
roti would represent the pass percentage?
2. Students write examinations either in Urban Centres or
Rural Centres. What part of the roti would represent
the percentage of students who have passed from Rural
Centres?
3. Take another roti. Can you show the percentage of boys
who have secured a first class?

21


Reading a Picture

A chart can be of many kinds.
It is an easy-to-understand representation of information.
A chart in mathematics can be very helpful. Take a look at the
chart presented here. The vertical line shows average marks of a
class, 0 to 100. Average=Sum of the marks of all the students in
the class divided by the number of students.
• If the sum of marks of 40 students is 2800, then the class
average is 70 marks.
• The coloured blocks represent the four Quarterly (Qtr)
Examination marks obtained by each class.
• Just by looking at the picture, what are the things that you
can learn about the three classes?
22

1. Which class has shown the most improvement?
2. Have students of Class 4 improved?
3. What can you say about Class 5 students?
When you see different shapes around you, study them.
See if there is anything special about these shapes.
Then you can record your observations in the form of charts.

Different types of charts

Pie Chart

Bar Graph

Divided Bar Graph

Line Graph
23